Markov Simulation: NBA Playoffs Round 2

In continuation of our Markov simulation of the NBA Playoffs, we take a look at the updated probabilities for each team remaining. In this article, we take a cursory look at each second round match up and see how the first round panned out compared to the probabilistic predictions.

So Far So Good: All rounds predicted within confidence

Of the eight first round match-ups, our probabilistic models correctly picked 7 of the 8 winners. The one missed team? The Utah Jazz, who was had the statistical expectation of losing game 7 by a slim margin. The Jazz did indeed go to game seven, but managed to push ahead of the Blake Griffin-less Clippers. So why do we still claim victory?

By our Markov model, we are effectively simulating a random variable that only takes on values -4, -3, -2, -1, 1, 2, 3, 4. These values represent the win differential at the end of the series. The expected value is then the sum of the possible win differentials, each multiplied by their respective probabilities. For instance, the Golden State Warriors vs. the Portland Trailblazers, we obtained an expected value of 2.12 or Golden State winning by 3 games, hence the 4-1 prediction. Due to the discrete nature of the probability distribution, we cannot just “add standard error” but rather look for tightest region of probability that will contain the expected value (since the distribution is unimodal). So what in the world does this mean???

Let’s walk through this quickly to understand the numbers and what they really mean. The value of 4 has a probability of 23.5619% while the value of 3 has a probability of 28.5843% and the value of 2 has a probability of 21.6732%. Note these values are Golden State Sweeps Portland, Golden State wins 4-1, and Golden State wins 4-2, respectively. In this case, the values of 2, 3, and 4 have probability 73.8195%. If we opted for 95% confidence, we would have an interval running from -2 through 4. So we do not look for 95% confidence. We actually just look for ~60% confidence. This makes the intervals tighter and more meaningful.

In this case, the confidence intervals for each first round series was:

  • Golden State Wins in 4 through 6 games.
  • Los Angeles Wins in 6 or 7 games; Utah Wins in 6 or 7 games.
  • Houston Wins in 5 through 7 games.
  • San Antonio Wins in 5 through 7 games.
  • Boston Wins in 5 through 7 games.
  • Washington Wins in 5 through 7 games.
  • Toronto Wins in 6 or 7 games; Milwaukee wins in 7 games.
  • Cleveland Wins in 4 through 6 games.

As we see, the confidence regions all hit their targets. We must stress that 60% confidence regions means that if we perform this analysis for millions of years, we should expect roughly 40% of these confidence intervals miss entirely. This does not mean that 4 out of 10 predictions are way off.

Second Round:

In the previous article, we noted that Houston was favored over San Antonio while Washington has a strong chance for an upset. So let’s walk through each second round match-up.

Golden State (71 – 15) vs. Utah Jazz (55 – 34)

Predicted Winner: Golden State Warriors in 5 games (Probability of Winning: 77.3492%)

The Utah Jazz picked up their upset series win over the Los Angeles Clippers in a series that was widely viewed as an equally stacked match-up. Interestingly, Utah played extremely well with Rudy Gobert’s injury while the Clippers picked up a big Game 6 win in Utah without Blake Griffin. Some folks will quickly write off the Jazz suggesting that their struggles to close out Game 6 on their home court shows they lack poise in big games. However, the Jazz have capable players and a resurgent Joe Johnson that is capable of grinding out games against the Warriors.

Over the season, the Warriors are 2-1 against the Jazz, with the Jazz picking up the win three weeks ago. However, despite the Jazz missing Gordon Hayward for the game, the Warriors were without Klay Thompson and sat their starters in the fourth despite Golden State hanging on to a 1-point lead with 7 minutes to go. Gobert, George Hill, and Johnson managed to dominate the remainder of the game to win by six.

In order for the Jazz to win, they will have to control the pace of the game, attack Steph Curry on defense after spreading the court to pull Thompson and Durant away from help, and to control the paint. With Pachulia/McGee and Draymond Green settling in the post, Gobert will have his hands full trying to stay in the paint on defense; particularly when the Warriors bring in Iguodala to go small.

The Jazz will rely on Hill and Johnson to keep defenders honest in an effort to force Kevin Durant to guard up Gordon Hayward. By doing so, Durant will get worked hard on both ends of the court, potentially limiting his minutes. However if this poses a problem, expect Durant to switch off Hayward in favor of Iguodala and cover Ingles for a handful of possessions.

Key Players: Rudy Gobert, Gordon Hayward, Andre Iguodala

Gordon Hayward is the key player in this series overall. In his lone match-up against the Warriors, Hayward was 2-10 for six points in a rather uninspiring 27 minutes of action. Rudy Gobert managed to turn in a couple double-doubles, but will need to come up bigger than 17 and 12 in this series to help advance the Jazz’s hopes.

For the Warriors, Iguodala’s ability to move the defense from big to small and vice-versa will give Golden State the needed flexibility to adapt against the game plan of Quin Snyder. This series should be too much for the Jazz; but it will be interesting to see the adjustments made over the series to see how competitive they will be.


San Antonio Spurs (65 – 23) vs. Houston Rockets (59 – 28)

Predicted Winner: Houston Rockets in 6 games (Probability of Winning: 55.7508%)

This is the marquee match-up of the second round. Of the four teams most likely to win the NBA finals; with the others being Cleveland and Golden State, the Rockets and Spurs should not fail to deliver on entertainment. In this series, we find ourselves with the same score of style with the Spurs and the up-tempo fury of the Rockets. While this series should give some throw-back to the intense Spurs-Suns playoff series nearly a decade ago, we see a stronger challenge thrown at the Spurs.

First off, James Harden is extremely difficult to guard. With his ability to get to the basket, placing a player such as Kawhi Leonard may spell disaster for the Spurs. Harden enjoys running off a high screen set that either sets up a pick-and-roll offense or a pick-and-pop with a scorer. For those plays, if Leonard is guarding Harden the screen will force either a strong show from the screen defender or give up the lane entirely. The method to attempt to stop this is to place a weaker guard on Harden and sag in protection to entice Harden to score 60 points from the mid-range. If in case, he starts doing this, then help can crash from the strong defenders such as LaMarcus Aldridge, Danny Green, or Kawhi himself.

In reality, Danny Green will most likely take on the role of limiting Harden on defense as Leonard or Tony Parker will find themselves on Patrick Beverly. This leaves the biggest question mark of the series… who does LaMarcus Aldridge cover? Covering Ryan Anderson, Aldridge will find himself being run ragged inside and out in attempt to cover Anderson. Covering Trevor Ariza would lead to moving Kawhi Leonard to guarding a more difficult player, leading to potential loss of transition into offense. This means the key players of this series will be LaMarcus Aldridge, Danny Green, Ryan Anderson, and Trevor Ariza. In fact, I would actually suggest the entire three-point squad for Houston versus containment and help-side rotation of the Spurs.

That said, LaMarcus came to the Spurs to win a title. Aldridge has yet to get San Antonio over that proverbial hump and if his playoff woes over the years continue; expect Houston to race out to a lead. This series will be all about pace. If Houston opens up the court, expect Harden to do damage in the paint; allowing for shooters to be open all night long.


Boston Celtics (57 – 31) vs. Washington Wizards (53 – 35)

Predicted Winner: Boston Celtics in 6 games (Probability of Winning: 54.8728%)

The Wizards and Celtics won their first round series, but made it look difficult. The Celtics were dominated by Robin Lopez and let Jimmy Butler shoot at will over them. After dropping the first two games, an injury to Rajon Rondo and the lack of depth doomed Chicago over the final four games of their series. The downfall of the Bulls overshadowed Avery Bradley’s strong finish to the series and eventual putting Boston back on the map as a potential contender.

Now the Celtics are rewarded with facing off probably the best back-court duo in the Eastern conference in John Wall and Bradley Beal. The Celtics are built for such a match-up. In our previous article, we noted that the weaknesses for the Celtics revolve around interior post-presence, rebounding, and covering screens involving versatile big players. While the Bulls had that to an extent, they effectively only had Robin Lopez. The Wizards have Marcin Gortat and Markieff Morris. The Wizards are desperately missing Ian Mahinmi for this series as their depth in the position Boston is most vulnerable at is thin.

If the Wizards are going to have a shot at taking the series, they will need their bigs to step up. Otto Porter Jr. will have to play more like a four and get boards. Jason Smith will need to play a bigger role in limiting Al Horford and Amir Johnson. The match-ups for the Wizards don’t bode well. Despite this, the Wizards strong guard play will give them chances to wear down the Celtics’ Isaiah Thomas, Avery Bradley, and Marcus Smart.

This means that the key players are Jae Crowder and Otto Porter Jr. Both players will likely find themselves matched up on each other throughout this series. However, Crowder is needed on the wing while Porter Jr. will be needed as extra rebounding presence to help Morris and Gortat. If Crowder has big contributions on offense, the Wizards will lose their rebounding presence. Similarly, if the Wizards maintain a rebounding presence, expect the Celtics to get open looks from outside.


Cleveland Cavaliers (55 – 31) vs. Toronto Raptors (55 – 33)

Predicted Winner: Cleveland Cavaliers in 5 games (Probability of Winning: 70.2235%)

The Cavaliers looked strong in finishing out a Paul-George-led Indiana Pacers squad in a quick four game series. Their reward is to face a Toronto Raptors team that struggled with an athletic and motivated, young Milwaukee Bucks squad that was a couple missed open jump shots away from pushing this series to seven games; if not a series win. Toronto has been Helter Skelter these playoffs. Jonas Valanciunas was one of our key players last series and he never really showed up.

The Raptors are 1-3 against the Cavaliers this season, with the lone win coming with LeBron James, Kyrie Irving, and Kevin Love all sitting out. The Raptors are in trouble this series if they don’t figure out how to get Valanciunas integrated into the offense.

The Raptors have a solid back-court highlighted by DeMar DeRozan and Kyle Lowry. One of which will be forced to cover Kyrie Irving all night long. Most likely Lowry. This means DeRozan will be stuck being either covering J.R. Smith; which is his best option, or rotated off onto James or Love. The Cavaliers, a team that loves to run the Horns-Twist offense, will get at least 1-2 defensive rotations per offensive possession, allowing them to always find at least one mismatch; be it Irving covered by Serge Ibaka or James covered by Lowry. Either way, the Cavaliers pose more match-up nightmares for the Raptors than any other team can in the playoffs.

Unless P.J. Tucker plays lights out or DeMarre Carroll finds his Atlanta Hawk abilities, expect this series to be over relatively quickly. Hence the key players are DeMarre Carroll, P.J. Tucker, and again Jonas Valanciunas. These guys need to help the Toronto back-court and will be the help defenders on almost every pick-play.


Conference Finals!

This means our expected conference finals will be the Golden State Warriors versus the Houston Rockets and the Boston Celtics versus the Cleveland Cavaliers. Without examining the match-ups in depth (we’ll save that for later), we find that the current projections are

Golden State over Houston in 6 games.

Cleveland over Boston in 6 games.

In fact, here are the probabilities for each team making the NBA finals:

  • Eastern Conference
    • Cleveland Cavaliers: 43.9046%
    • Boston Celtics: 26.5036%
    • Washington Wizards: 17.2224%
    • Toronto Raptors: 12.3694%
  • Western Conference
    • Golden State Warriors: 49.7782%
    • Houston Rockets: 24.8739%
    • San Antonio Spurs: 17.4320%
    • Utah Jazz: 7.9159%

NBA Finals

The Golden State Warriors are still projected to be the NBA Champions. As usual, each round, we will adjust the probabilities. Here are the current probabilities.

  • Golden State Warriors: 36.3214%
  • Cleveland Cavaliers: 18.4155%
  • Houston Rockets: 15.4878%
  • San Antonio Spurs: 9.9116%
  • Boston Celtics: 8.9735%
  • Washington Wizards: 4.3901%
  • Utah Jazz: 3.5578%
  • Toronto Raptors: 2.9423%



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